ORTHOGONAL Frequency Division Multiplexing

Transcription

1 Improving OFDM Data Estimation by Overlapping Base Cyclic Prefix Reuse Klaus ueske an Jürgen Götze Information Processing Lab, EE/IT TU Dortmun University, Dortmun, Germany Abstract Ortogonal Frequency Division Multiplexing (OFDM) enables ig trougput ata transmissions over frequency selective faing cannels. Using a cyclic prefix te transmission cannel can be escribe by circular convolution, wic allows low complexity FFT base receiver implementations. Generally te is iscare at te receiver prior to ata estimation, i.e. te reunancy containe in te is lost. Tis reunancy, owever, can be use to improve ata estimation an ence reuce te bit error rate of te transmission system. Tis paper consiers overlapping frequency omain equalization to exploit reunancy for improve OFDM ata estimation. I. INTRODUCTION ORTOGONAL Frequency Division Multiplexing (OFDM) is wiely use in ig spee wireless communication systems. Te main reasons are OFDM s low receiver implementation complexity an its ig robustness to frequency selective cannel effects [1. Consiering tis, it is not a surprise tat OFDM is applie in most currently use transmission systems, like DVB, DAB, WLAN an DRM. Te corresponing multiple access sceme, OFDMA, is use in WiMax an 3GPP LTE. An important aspect of OFDM is te cyclic prefix: On te one an it works as a guar perio between OFDM symbols preventing inter symbol interference (II). On te oter an it transforms te linear cannel convolution into a circular convolution enabling low complexity FFT base receiver implementations. owever, te will reuce te acievable ata trougput, as no information payloa can be transferre wen transmitting te. In te WLAN stanar, for example, 20 % of te transmission time is allocate for te [2. Furtermore transmission energy is waste as te is iscare at te receiver an oes not contribute to ata estimation. One approac to tackle tis problem is te use of cannel equalizers in te receiver instea of s to remove II between OFDM symbols. In [3 we propose an overlapping frequency omain equalizer (FDE) tat can be use as pre-fft equalizer in a free OFDM transmission systems, referre to as Ov- OFDM [4. Te avoiance of, owever, requires moifications at te transmitter, wic cannot be realize wen ealing wit existing transmission stanars. In tese cases te aitional information in te can be use to improve te quality of te ata estimation, instea of iscaring it at te receiver. Corresponing approaces can be ivie into two categories: Metos tat exploit only parts of te tat are free of interference, i.e. te cannel lengt is sorter tan te ([5 [6), an metos tat can use te full to improve ata estimation [7. Te latter can acieve maximum NR improvement, owever, tey also require more complex II cancellation prior to averaging te reunant ata. In [7 an initial ata estimation is obtaine by conventional OFDM emoulation, wic is ten use for II cancellation, followe by a secon ata estimation step using te reunancy. owever, ue to its structure tis approac is prone to error propagation. In tis paper te overlapping FDE escribe in [3 is use to remove II to improve ata estimation by exploiting reunancy using te full. Two approaces will be escribe: Te first one, referre to as overlapping reuse, is realize by completely equalizing te receive -OFDM signal witout iscaring te. Tis yiels two inepenent estimates for te ata block, one in front an one at te en of eac symbol. By averaging tese estimates, wic are affecte by uncorrelate noise, te signal to noise ratio (NR) can be increase. Te secon one, referre to as overlay reuse, equalizes solely te parts in front an at te en of eac symbol. Tese can be use to compute a correction factor tat will be ae to te frequency omain estimates obtaine by conventional OFDM to improve ata estimation quality. Te paper is organize as follows: In ection II a ata moel for OFDM transmission will be introuce. A sort introuction to overlapping FDE is given in ection III. Te application of overlapping FDE for reuse is escribe in ection IV. imulation results are use to compare te bit error rate (BER) of conventional OFDM an OFDM wit reuse in ection V. An important aspect is te

2 computational complexity, wic is consiere in ection VI. Conclusions are rawn in ection VII. II. OFDM YTEM MODEL Te moel escribes te transmission of a moulate ata vector C V of lengt V over a time ispersive wireless cannel, wic is escribe by its normalize iscrete impulse response C L of lengt L. Te cannel is assume to be time invariant uring te transmission of. Te noise vector n is obtaine by sampling a wite Gaussian noise process wit power σ 2. Te OFDM symbols are obtaine by separating into segments of lengt, wic are ten transforme to time omain by an IFFT (Inverse Fast Fourier Transform) of size. Te resulting vector containing te OFDM symbols in time omain is enote by t. Te receive vector x t C V +L 1 can be compute by convolution of t wit. By using te cannel convolution matrix C (V +L 1) (V ) te moel can be summarize in x t = t + n. (1) Te receiver as to compute an estimate ˆ of te transmitte ata. A cyclic prefix of at least N cp = L 1 samples perioically inserte between consecutive OFDM symbols avois interference an splits te matrix up into smaller circular submatrices s of size. Wit F s te Fourier matrix of size tese submatrices can be represente by teir EVD (Eigenvalue Decomposition) as s = s ΛF s. Te iagonal matrix Λ contains te eigenvalues of s. Wit tis te receive signal for one OFDM symbol is given as x t,s = s Λ t,s + n. (2) Demoulation is performe by a single Fourier transform an multiplication by a iagonal matrix : ˆ = F s x t,s (3) Te matrix = (Λ Λ + σ 2 I) 1 Λ escribes te minimum mean square error (MME) equalizer in frequency omain. Note tat all erivations can be simply moifie to support least squares (L) estimation or maximum ratio combining (MRC) [1. III. OVERLAPPING FDE Instea of using s te interference between consecutive OFDM symbols coul be remove using an equalizer prior to emoulation. Given te receive signal in Eq.(1), te MME equalizer in time omain is given as ˆ t = ( + σ 2 I) 1 x t. (4) After equalization te estimates ˆ of te originally transmitte ata can be obtaine by symbol-wise application of an FFT of size to ˆ t. Due to missing s an efficient computation of Eq.(4) using inepenent block submatrices is not straigtforwar. owever, wat appens if we still perform block-wise equalization in te receiver, i.e. equalize a ata block x t,b of size using te matrix B like sown in Figure 1? Fig. 1. x t,b = B cyclic extension t,b + n Block construction for overlapping equalization. Tis consequently results in interference tat will corrupt te estimate ata. owever, ue to te finite cannel lengt we can expect tat te istorting influence of te neigboring blocks is more significant in te borer parts of te equalize blocks [3. To illustrate tis, te ensemble-average equalization error for tree neigboring blocks is epicte in Figure 2(a). Fig. 2. Ensemble-average equalization error a) b) c) Inex Error istribution for overlapping equalization. Tis battub like error istribution can be exploite by using overlapping ata blocks instea of neigboring blocks, i.e. a block wit elements n,..., n + is followe by a block n +,..., n + 2, as epicte in Figure 2 (b). ere escribes te lengt of te overlapping parts. Te equalization error can ten be reuce by omitting te overlapping, more erroneous outer parts of eac block an selecting te mile parts for

3 furter processing. Te resulting ensemble-average equalization error of te output sequence is epicte in Figure 2(c). To allow te use of efficient FFT base EVD algoritms for MME equalization te overlapping block matrices are cyclically extene, wic results in signal processing structures similar to tat of conventional -OFDM systems. Te MME-FDE for one block is ten given as ˆ t,b = B F B x t,b. (5) After equalization te mile parts of ˆt,B are selecte an combine to obtain te entire equalize output sequence ˆ t. IV. REUE Instea of iscaring it at te receiver, te can be use to improve ata estimation by averaging inepenent estimates of te itself an te corresponing ata part at te en of te OFDM symbol. Tese can be obtaine using te overlapping FDE escribe in te previous section. A. Overlapping Reuse Te receive sequence incluing te s is partitione into overlapping parts x t,b of lengt. Tese parts are ten equalize corresponing to Eq.(5). Te combine output sequence now contains two inepenent estimates of te ata, wic can be simply average to improve ata estimation: [ 0 Is c 0 ˆ = F s 1 2 I 1 c 0 2 I c ˆ t,s+c. (6) ere ˆ t,s+c enotes one equalize OFDM symbol plus taken from ˆ t an I c is te unity matrix of size N cp. After averaging OFDM emoulation is performe by symbol-wise Fourier transform. Te resulting receiver structure an overlapping sceme are epicte in Figure 3(b). For comparison te conventional OFDM system is given in Figure 3(a). B. Overlay Reuse Using overlapping FDE one OFDM symbol will be partitione into several parts of lengt wit <. Tis means tat remaining equalization errors in te borer parts of all tese blocks can egrae te quality of ata estimation. It woul be esirable to apply Eq.(5) only for parts tat really ave to be equalize, i.e. use normal OFDM ata estimation for te main part of te symbol an apply equalization only for te parts. Te ata insie te OFDM symbol can be equalize by a) Conventional OFDM: b) Overlapping reuse: OV c) Overlay reuse: Fig. 3. x f x r x f F B F B B B Comb. el x r F F Aver. F ˆ ˆ Time F ˆ Block iagram of ifferent OFDM receivers. Time simple cyclic prefix base FDE. Tis leas to ˆ t,o = s F s x t,s. Te equalize can be irectly obtaine from Eq.(5). Wit tis te averaging can be escribe as ˆ = F s ([ Is c I c ˆ t,o + [ I c ˆ t,s ). Te -FDE equalization can be avoie to reuce computational complexity. In a first step te previous equation will be rearrange to ˆ = F s x t,s (7) ([ [ ) F s I ˆ t,o + c I ˆ t,s. c Te first part escribes conventional OFDM estimation, te secon part can be seen as a correction factor, referre to as overlay. It is obvious tat only te equalize part in te rear of ˆ t,o is require, wic can be simply obtaine from Eq.(5). Consiering tis te overlay approac can be escribe as ˆ = F s x t,s (8) [ F s I P B F B (x t,f x t,r ). c Te vectors x t,f an x t,r are suitable inputs for te equalizer to obtain te equalize parts in front an at te en of eac OFDM symbol. Te matrix P is a permutation matrix tat sifts te usable mile part of eac equalize block (wic contains te equalize ) to te en of te symbol. Note tat for tis approac te overlap-select-combine proceure of te overlapping FDE simplifies to a single select an sift operation. Te resulting receiver structure

4 an te use parts of te receive sequence are epicte in Figure 3(c). Note tat te upper signal pat sows a conventional OFDM receiver an te lower pat computes te overlay. Depening on te actual NR te overlay pat can be simply activate to improve te ata estimation or eactivate to reuce computational effort. V. IMULATION REULT Te simulation results were generate using a symbol space multi pat faing cannel moel [8. Position an average power of te cannel taps are cosen accoring to ETI cannel P6 [9. To moel single frequency network (FN) beavior tese taps are repeate wit lower power at position N cp /2, as sown in Figure 4 for N cp = 256. Te cannel NR i (B) =10 log 10 ( P P N ) (9) =10 log 10 ( P N N cp P =NR(B) + 10 log 10 ( P ) N Ncp N cp ). 2 Te NR improvement compare to conventional OFDM for ifferent ratios N cp / is given in Table I. Assuming a ratio N cp / = 1/4 (e.g. WLAN or TABLE I NR GAIN FOR DIFFERENT RATIO N cp/. N /N 1/4 1/8 1/16 1/32 NR gain/b Average Power [B Delay [T Fig. 4. Average Power of Cannel Taps for N cp = 256. DVB-T), an NR improvement of more tan 1/2 B can be acieve, wic is also visible in te simulation results given in Figure 5 for a wie range of E b /N 0. Bit error rate Conventional OFDM Overlapping reuse Overlay reuse coefficients are assume to be time invariant uring te transmission of one ata vector an are known at te receiver. Te subcarriers are QPK (Quarature Pase ift Keying) moulate. Prior to transmission te ata is encoe using a convolutional coe wit constraint lengt K = 7 an coe rate R = 1/2. Decoing is performe by a Viterbi ecoer using soft inputs. Te parameters are cosen as = 4N cp, D = 0.75N cp for te overlapping reuse approac an = 2N cp, D = 0.5N cp for te overlay approac. Note tat block size an overlapping lengt D are esign parameters tat allow a traeoff between equalization error an computational complexity. Exploiting te reunancy will increase te NR of te receive signal. Wen averaging te part in front an at te en of eac symbol te signal power remains unaltere, wile te noise power will be reuce. Uner te assumption of perfect II cancellation te improve NR can be calculate as te ratio between signal power P an mean noise power P N, i.e. Bit error rate E B /N 0 in [B Conventional OFDM Overlapping reuse Overlay reuse E B /N 0 in [B Fig. 5. BER of conventional OFDM an OFDM wit reuse for = 2048 wit N cp = 256 (top) an N cp = 512 (bottom).

5 For larger E b /N 0 te improvement ue to noise averaging will be countervaile by te remaining equalization error of te overlapping FDE. Tis beavior is more significant for te overlapping reuse approac, as several blocks are require to equalize one OFDM symbol. owever, as te main benefit of reuse is in te lower E b /N 0 regions, tis beavior is not a limitation. VI. COMPUTATIONAL COMPLEXITY Te complexity of all tree consiere OFDM transmission systems is ominate by te FFT an te inverse FFT respectively. Wit N 2 log 2 N te number of complex multiplications require to compute one FFT, te total number of multiplications per symbol necessary for a conventional OFDM system normalize to is given by M OFDM = log 2. (10) Due to overlapping in te first approac, more ata blocks ave to be processe by te equalizer, so te total number of multiplications is given by M 1 = 1 2 log Ncp 1 (log 2 + 1). (11) Te overlay reuse requires equalization of te part for eac symbol. Tis sums up to M 2 = 1 + log 2 + (log 2 + 1). (12) Table II sows te number of require multiplications for ifferent ratios N cp /. Te symbol lengt is set to N = 2048, te equalizer parameters an D are cosen accoring to ection V. TABLE II MULTIPLICATION PER YMBOL WIT = 2048 AND DIFFERENT RATIO N cp/. N cp / Conv. OFDM Overlapping Overlay 1/ / / / Te complexity of conventional OFDM oes not epen on te cosen lengt. owever, for reuse te ratio N cp / significantly influences te amount of computational overea. For bot consiere approaces te complexity grows wit increasing lengt, toug te complexity of te overlapping approac is significantly iger compare to te overlay approac. Te reason for tis lies in te ifferent concepts: Wile for te overlay approac only one aitional block as to be compute for eac OFDM symbol, several blocks are require for te overlapping approac. Furtermore, larger values for an D ave to be cosen for te overlapping approac to acieve similar BER performance. Using overlay reuse significant NR improvements can be acieve wit a reasonable increase in computational complexity by a factor of 2. Note tat te computational complexity of te overlay meto can be furter reuce by FFT pruning metos as many FFT inputs are zero. VII. CONCLUION In tis paper overlapping FDE was use to exploit reunancy in te to improve ata estimation in OFDM receivers. Wile te overlapping approac as a comparatively ig computational complexity, te overlay approac can significantly improve te BER wit reasonably increase computational complexity. Wit te propose metos te coverage area of a wireless network (DVB-T or WLAN) can be increase ue to NR improvement especially in te low NR region. REFERENCE [1 R. van Nee an R. Prasa, OFDM for Wireless Multimeia Communications, Artec ouse Publisers, [2 IEEE, t a part 11: Wireless LAN meium access control (MAC) an pysical layer (PY) specifications. ig-spee pysical layer in te 5 Gz ban, Tec. Rep., IEEE, [3 C. V. inn an J. Götze, Computationally efficient block transmission systems wit an witout guar perios, ignal Processing, Elsevier Nort-ollan, Inc., vol. 87, no. 6, pp , [4 K. ueske an J. Götze, Ov-OFDM: A reuce PAPR an cyclic prefix free multicarrier transmission system, in Proc. IEEE Int. ymposium on Wireless Communication ystems (IWC), iena, Italy, eptember [5 G.E. Bottomley an L.R. Wilelmsson, Recovering signal energy from te cyclic prefix in OFDM, IEEE Transactions on Veicular Tecnology, vol. 57, no. 5, pp , ept [6 A. Tarigat an A.. aye, An optimum OFDM receiver exploiting cyclic prefix for improve ata estimation, in IEEE International Conference on Acoustics, peec, an ignal Processing (ICAP), [7 L. Vangelista, M. Rotoloni, an A. Morello, Improve ata etection exploiting full cyclic prefix for te evolution of DVB-T, in Int. Wireless Communications an Mobile Computing Conference (IWCMC), 2008, pp [8 K. Ruttik, A wieban raio cannel moel for simulation of caotic communication systems, in Proceeings of ECCTD, Buapest, August 1997, pp [9 ETI TR V1.3.1, Digital Vieo Broacasting (DVB): Implementation guielines for DVB terrestrial services: Transmission aspects, Tec. Rep., ETI, 2008.